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2018 Projections of spherical Brownian motion
Aleksandar Mijatović, Veno Mramor, Gerónimo Uribe Bravo
Electron. Commun. Probab. 23: 1-12 (2018). DOI: 10.1214/18-ECP162


We obtain a stochastic differential equation (SDE) satisfied by the first $n$ coordinates of a Brownian motion on the unit sphere in $\mathbb{R} ^{n+\ell }$. The SDE has non-Lipschitz coefficients but we are able to provide an analysis of existence and pathwise uniqueness and show that they always hold. The square of the radial component is a Wright-Fisher diffusion with mutation and it features in a skew-product decomposition of the projected spherical Brownian motion. A more general SDE on the unit ball in $\mathbb{R} ^{n+\ell }$ allows us to geometrically realize the Wright-Fisher diffusion with general non-negative parameters as the radial component of its solution.


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Aleksandar Mijatović. Veno Mramor. Gerónimo Uribe Bravo. "Projections of spherical Brownian motion." Electron. Commun. Probab. 23 1 - 12, 2018.


Received: 1 June 2018; Accepted: 8 August 2018; Published: 2018
First available in Project Euclid: 1 September 2018

zbMATH: 06964395
MathSciNet: MR3852266
Digital Object Identifier: 10.1214/18-ECP162

Primary: 58J65 , 60H10

Keywords: non-Lipschitz stochastic differential equation , Pathwise uniqueness , Skew-product decomposition , Wright-Fisher diffusion


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